Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+9y &= -9 \\ -x-y &= 9\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = y+9$ Divide both sides by $-1$ to isolate $x$ $x = {-y - 9}$ Substitute this expression for $x$ in the first equation. $3({-y - 9}) + 9y = -9$ $-3y - 27 + 9y = -9$ Simplify by combining terms, then solve for $y$ $6y - 27 = -9$ $6y = 18$ $y = 3$ Substitute $3$ for $y$ in the top equation. $3x+9( 3) = -9$ $3x+27 = -9$ $3x = -36$ $x = -12$ The solution is $\enspace x = -12, \enspace y = 3$.